A183909 Number of nondecreasing arrangements of n+2 numbers in 0..6 with each number being the sum mod 7 of two others.

1, 1, 22, 136, 470, 1193, 2525, 4752, 8238, 13438, 20912, 31340, 45538, 64475, 89291, 121316, 162090, 213384, 277222, 355904, 452030, 568525, 708665, 876104, 1074902, 1309554, 1585020, 1906756, 2280746, 2713535, 3212263, 3784700, 4439282, 5185148

Offset

1,3

Comments

Column 6 of A183912.

Links

R. H. Hardin, Table of n, a(n) for n = 1..76

Formula

Empirical: a(n) = (1/720)*n^6 + (11/240)*n^5 + (89/144)*n^4 + (209/48)*n^3 - (13003/360)*n^2 + (531/10)*n + 12 for n>3.

Conjectures from Colin Barker, Apr 06 2018: (Start)

G.f.: x*(1 - 6*x + 36*x^2 - 32*x^3 - 20*x^4 + 3*x^5 + 40*x^6 - 16*x^7 - 9*x^8 + 4*x^9) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10.

(End)

Example

All solutions for n=2:
..0
..0
..0
..0

Crossrefs

Cf. A183912.

Sequence in context: A254698 A041936 A254699 * A263481 A238170 A275799

Adjacent sequences: A183906 A183907 A183908 * A183910 A183911 A183912

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved